On the Brightness of an Object and that of its Image. 505 



An J if the solid angles are a> b o> 2 



(Oi di sin i _ n 2 cos r 

 (o 2 ~~ dr sin r fii* cos i ' 



Now let I x be the luminosity of s, and I 2 that of the surface 

 R T as seen in the medium ]i 2 by the light coming originally 



from s. I x is the luminosity RT must have to send back to s 

 the same amount of light as s sends to it, that is, as R T sends 

 on into fi 2 . If s x is the area of the surface RT, the quantities 

 of light received and sent on by it are 



I, 5x0)! cos i, and I 2 s x (o 2 cos ?'. 



And these are equal. Thus from above 



Ii :I 2 =/*i 2 :/i2 2 . 



In the same manner the luminosity of the second surface 

 across which the rays pass, as seen in the third medium of 

 index fi s , is proportional to fi 3 2 ; and so on. 



If the rays on passing across the last surface form a true 

 image of s, so that the combination of surfaces is aplanatic for 

 5, the brightness of this image is the same as that of the last 

 surface ; for it subtends the same solid angle at the point of 

 view as the portion of the surface which sends the same 

 quantity of light to the point of view. Thus, if /-t, pJ are the 

 refractive indices of the medium in which the object is and 

 that in which the eye is which sees the image, and T, V the 

 luminosities of the object and image ; 



